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Quantitative modelling of financial risks
Pavel V. ShevchenkoQuantitative Risk Management
CSIRO Mathematical and Information Sciences
Australia-Japan Workshop on Data ScienceKeio University, 24-27 March 2009
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Financial Risk in QRM
CMIS Quantitative Risk Management (QRM) group:• 20 researchers www.cmis.csiro.au/QRM• Financial risk, infrastructure, security, air-transport• Activities/modes of engagement: research, consulting, model
development/validation, software developmentFinancial risk team in QRM: 6 researchersIndustry: banks, insurance/electricity companies, hedge fundsBeneficiaries of our work in risk management:• Financial institutions and their shareholders (risk reduction)• Stability of banking/insurance systems• Science and CMIS (reputation, external earnings, IP)Our mission – To conduct research in financial risk quantification,
measurement and calculation; To develop innovative quantitativemethods and tools in financial engineering
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Track Records in Financial Risk since 1999
External Projects• Derivative pricing: option pricing software Reditus/Fenics since 1999• Operational Risk: risk engines for 2 major banks in Australia, validation,
model development and software development projects• Market Risk: validation and model development projects• Credit Risk: validation and model development projects• Insurance-Underwriting risk: consulting projects• Electricity: consulting projects• Commodities/interest rates: consulting projectsStrategic research projects: operational/credit/market risks, option pricing,
commodity/interest rate modelling, portfolio allocationCollaborators: Swiss Federal Institute of Technology (ETH Zurich), Vienna Uni
of Technology, Monash Uni, Cambridge Uni, UNSW, UTS, Macquarie Uni, Statistical Research Associates NZ.
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Links•Extreme Value models•Expert Elicitation•Combining expert&data•Bayesian methods•Dependence modelling•Numerical methods (PDE, MCMC, MC)•Time series analysis•State-space models•High performance computing•Optimisation
Other risk areas•Air transport•Ecology•Environment•Infrastructure •Security•Weather/Climate•Health
Financial Risk• Market Risk • Credit Risk • Operational Risk• Underwriting risk • Derivative pricing• Interest Rates• Trading strategies• Portfolio Management• Commodity/Energy• Carbon Trading• Liquidity risk
Financial risk and other risk areas
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Regulatory Requirements for banking industry
•Regulatory standards in banking industry:Basel Committee for banking supervision 1974Basel I, 1988: Credit Risk, Basel I Amendment 1996: Market Risk (VaR) Basel II 2001- ongoing: Credit Risk, Operational Risk
•Insurance regulation: International Association of Insurance SupervisorsJoint Forum on Financial Conglomerates 1996Solvency II (similar to Basel II for banks)
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Basel II• Basel II requires that banks hold adequate capital to protect
against Market risk, Credit risk and Operational Risk losses. Three-pillar framework:
Pillar 1: minimal capital requirements (risk measurement)Pillar 2: supervisory review of capital adequacyPillar 3: public disclosure
Advanced Measurement Approaches allow internal models for calculations of capital as a large quantile of loss distribution.Operational Risk is new risk category
• In Australia, the national regulator APRA is now applying the Basel II requirements.
• Solvency 2 for insurance industry
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Financial Risks – quantifying uncertainties
Risks are modelled by random variables mapping unforeseen future states of the world into values representing profits and losses.
Market Risk: modelling of losses incurred on a trading book due market movements (interest rates, exchange rates, etc)
Credit risk: modelling of losses from credit downgrades and defaults (e.g. loan defaults)
Operational Risk: modelling of losses due to failed internal processes, people or external events (e.g. human errors, IT failures, natural disasters, etc)
Quantifying the uncertainties: process uncertainty, parameter uncertainty, numerical error, model error
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Regulatory Requirements – Risk MeasuresValue at Risk (VaR)
loss probability density
0
0.01
0.02
0.03
0.04
0$ loss
Expected Loss
Unexpected Loss
10daysover 0.99 :kMarket Ris1year over :kCredit Ris year1over 999.0 : RisklOperationa
}1]Pr[:inf{ :measureRisk
loss expectedloss Unexpected
=••=•
−≤>=•
−=•
qxLossxVaR
VaR
q
q
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Market, Credit and Operational Risks
jXXN
jZ
XZZL
pIIX
IXLM
XSSSXZX
SSQ
K
jjN
jj
j
jN
i
jij
jj
iii
M
iii
tttttttttt
K
k
Mttttkt
risk for severities andfrequency annual theare ,..., and
risk todue loss annual theis
; :risk lOperationa
defaultof prob. is]1Pr[ ;0or1 default;givenloss is
:obligors of portfolio :riskCredit
)(,/)( ;
etc FX,s,commoditie stocks, ),...,();(
contracts financial of portfolio :riskMarket
)()(1
1
)(56
1
1
21
20110
2110
1
)()1(
∑=∑=•
===
∑ ×=•
+−+=−=+=
∑ ==Π
•
==
=
−−−−
=
βσμαασσμ
SS
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Basel II, Operational Risk
•Basel II defined Operational Risk as: the risk of loss resulting from inadequate or failed internal processes, people and systemsor from external events. This definition includes legal risk but excludes strategic and reputational risk.
•Losses can be extreme, e.g.1995: Barings Bank (loss GBP1.3billion)1996: Sumitomo Corporation (loss US$2.6billion)2001: September 112001: Enron, USD 2.2b (largest US bankruptcy so far)2002: Allied Irish, £450m2004: National Australia bank (A$360m)2008: Société Générale (Euro 4.9billion)
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Operational Risk Basel II Business Lines/Event Types
Basel II Business Lines (BL)• BL(1) - Corporate finance• BL(2) - Trading & Sales• BL(3) - Retail banking• BL(4) - Commercial banking• BL(5) - Payment & Settlement• BL(6) - Agency Services• BL(7) - Asset management• BL(8) - Retail brokerage
Basel II Event Type (ET)•ET(1) - Internal fraud:•ET(2) - External fraud: •ET(3) - Employment practices and
workplace safety: •ET(4) - Clients, products and
business practices•ET(5) - Damage to physical assets:•ET(6) - Business disruption and
system failures: •ET(7) - Execution, delivery and
process management:
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Loss Data Collection Exercise 2007 Japan - Annualized data: Number of events(100%=947.7) / Total Loss Amount (100%=JPY 22,650mln)
100% (no.events)100% (loss)
38.6%54.6%
10.9%3.9%
1.9%4.5%
8.8%24.8%
1.5%1.0%
36.5%8.3%
1.8%2.9%
Total
0.4%0.2%
0.02%0.00%
0.09%0.00%
0.13%0.00%
0.00%0.00%
0.02%0.00%
0.11%0.00%
0.09%0.18%
Other
3.5%2.0%
1.06%0.13%
0.18%0.04%
0.00%0.00%
1.40%0.53%
0.01%0.00%
0.00%0.00%
0.84%1.32%
BL(8)
2.1%1.5%
1.50%1.02%
0.05%0.00%
0.00%0.00%
0.48%0.49%
0.1%0.04%
0.00%0.00%
0.00%0.00%
BL(7)
5.3%3.8%
3.14%3.00%
1.19%0.22%
0.01%0.00%
0.92%0.62%
0.01%0.00%
0.00%0.00%
0.00%0.00%
BL(6)
0.6%0.1%
0.23%0.00%
0.38%0.04%
0.00%0.00%
0.00%0.00%
0.00%0.00%
0.00%0.00%
0.00%0.00%
BL(5)
25.7%45.4%
15.05%16.87%
5.87%3.22%
0.69%4.19%
2.02%18.32%
1.16%0.71%
0.64%1.99%
0.29%0.13%
BL(4)
57.2%21.5%
13.21%8.43%
2.83%0.26%
1.11%0.26%
3.62%4.77%
0.14%0.18%
35.73%6.36%
0.54%1.24%
BL(3)
4.7%25.2%
4.12%25.03%
0.26%0.00%
0.00%0.00%
0.22%0.09%
0.04%0.04%
0.00%0.00%
0.01%0.00%
BL(2)
0.5%0.3%
0.28%0.18%
0.07%0.04%
0.00%0.00%
0.11%0.09%
0.01%0.00%
0.01%0.00%
0.00%0.00%
BL(1)
TotalET(7)ET(6)ET(5)ET(4)ET(3)ET(2)ET(1)
Ban
k of
Jap
an, e
t al (
2007
)
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Loss Data Collection Exercise 2004 USA - Annualized data: Number of events(100%=18371) / Total Loss Amount (100%=USD 8,643mln)
Fede
ral R
eser
ve S
yste
m, e
t al (
2005
)
100.0%, 100.0% (US$)
3.2%0.6%
0.8%0.1%
35.3%9.6%
0.7%0.8%
0.7%1.4%
9.2%79.8%
7.6%1.7%
39.0%5.1%
3.40%0.9%
Total
8.0%70.8%
0.08%0.01%
0.07%0.05%
3.45%0.98%
0.02%0.44%
0.12%1.28%
0.40%67.34%
1.75%0.34%
1.66%0.3%
0.42%0.1%
Other
7.3%1.6%
0.20%0.07%
2.20%0.25%
0.01%0.00%
3.30%0.94%
1.38%0.33%
0.10%0.02%
0.06%0.03%
BL(8)
2.4%2.5%
0.09%0.01%
1.82%0.38%
0.04%0.01%
0.00%0.00%
0.13%2.10%
0.10%0.02%
0.26%0.02%
0.00%0.00%
BL(7)
5.1%1.1%
4.52%0.99%
0.14%0.02%
0.01%0.01%
0.31%0.06%
0.04%0.02%
0.03%0.01%
0.01%0.02%
BL(6)
4.5%0.6%
0.23%0.05%
0.01%0.00%
2.99%0.28%
0.05%0.02%
0.01%0.00%
0.04%0.01%
0.18%0.02%
0.44%0.13%
0.52%0.08%
BL(5)
5.1%1.8%
0.44%0.04%
0.02%0.00%
1.38%0.28%
0.03%0.00%
0.01%0.00%
0.36%0.78%
0.17%0.03%
2.64%0.70%
0.05%0.01%
BL(4)
60.1%12.3%
2.10%0.26%
0.69%0.06%
12.28%3.66%
0.21%0.21%
0.56%0.1%
4.41%4.01%
3.76%0.87%
33.85%2.75%
2.29%0.42%
BL(3)
7.3%8.6%
0.05%0.15%
6.55%2.76%
0.24%0.06%
0.03%0.00%
0.19%4.29%
0.17%0.05%
0.01%1.17%
0.02%0.10%
BL(2)
0.3%0.5%
0.01%0.00%
0.03%0.01%
0.12%0.05%
0.00%0.00%
0.08%0.30%
0.06%0.03%
0.01%0.00%
0.01%0.14%
BL(1)
TotalFraudOtherET(7)ET(6)ET(5)ET(4)ET(3)ET(2)ET(1)
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Internal
Loss Data
External
Loss Data
Scenario analysis
Risk Frequency and Severity distributions
Annual loss distribution (per risk and over all risks)
Annual Capital Charge (Capital Allocation, sensitivity, what if scenarios)
Business environment and internal control factors
Insurance Dependence between risks
Operational Risk - Loss Distribution Approach
Monte Carlo simulations
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Operational Risk: Combining internal data, industry data and expert opinions
• BIS (2006), p.152: “Any operational risk measurement system must have certain key features to meet the supervisory soundnessstandard set out in this section. These elements must include the use of internal data, relevant external data, scenario analysis and factors reflecting the business environment and internal controlsystems.”
• An interview with four industry’s top risk executives: Davis, E. (1 September 2006). Theory vs Reality, OpRisk and Compliance: “[A] big challenge for us is how to mix the internal data with external data; this is something that is still a big problem because I don’t think anybody has a solution for that at the moment.” Or: “What can we do when we don’t have enough data [. . .] How do I use a small amount of data when I can have external data with scenario generation? [. . .] I think it is one of the big challenges for operational risk managers at the moment”.
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Ad-hoc procedures for combining internal data, industry data and expert opinions (SA)
)]ˆvar(:min[argˆ;1...,ˆ...ˆˆ.estimators moreor threecombine toextendedeasily be Can
ˆ,ˆ:)ˆvar( minimize to weightsChoose
)1()ˆvar(;1,ˆˆˆ :estimator unbiased Combined
.2,1,]ˆvar[;]ˆ[ i.e. ,parameter for ˆ and ˆ estimatest independen unbiased woconsider t : varianceMinimum
)()1()()(:onsdistributi Mixingseverity estimate data to external&internal
of sample combined andfrequency estimate data to Internal
111
22
21
21
222
21
22
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21212211
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21int21
totKKKtot
tot
tottot
mmm
extSA
wwwwww
ww
wwwwww
mE
xFwwxFwxFw
θθθθ
σσσ
σσσθ
σσθθθθ
σθθθθθθ
==++++=
+=
+=
−+==++=
===
•−−++•
•
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Combining three data sources: internal&externaldata and expert opinion via Bayesian inference
ion)approximat Gaussian methods, MCMCpriors, (conjugatedensity posterior -),|(
opinionsexpert of likelihood- )|(nsobservatio internal of likelihood-)|(
dataindustry by estimated is ondistributiprior -)(
)()|()|(),|(
),...,,( ),...,,( ),...,,(sParameter opinions Expert data Internal
2
1
21
212121
υXθθυθX
θ
θθυθXυXθ
θυX
π
π
ππ
θθθυυυ
hh
hh
XXX KMn
∝
===
Joint work with ETH Zurich: H. Bühlmann, M.Wüthrich, D.Lambrigger
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Combining internal & external data with expertExample: Poisson-Gamma-Gamma
5.0)|(,7.0ˆ:Expert15.0,41.33/2]75.025.0Pr[,5.0][:data External
(0.6) from 0) 2, 1, 1, 2, 0, 1, 1, 1, 0, 1, 0, 0, 0, (0, :counts Annual
==≈≈⇒=≤≤=
=
λυυβαλλ
VcoE
PoissonN
year
Arr
ival
rate
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Modelling dependence
•Basel Committee statement“Risk measures for different operational risk estimates must be added for purposes of calculating the regulatory minimum capitalrequirement. However, the bank may be permitted to use internally determined correlations in operational risk losses across individual operational risk estimates, provided it can demonstrate to the satisfaction of the national supervisor that its systems for determining correlations are sound, implemented with integrity, and take into account the uncertainty surrounding any such correlation estimates (particularly in periods of stress). The bank must validate its correlation assumptions using appropriate quantitative and qualitative techniques.” BIS (2006), p.152.
•Remark: Adding capitals implies perfect positive dependence between risks which is too conservative
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Dependence between risks
Sampler) (Slice via MCMCncalibratio :)parameters c(stochasti profilesrisk thebetween Dependence•
, and losses annual thebetween Dependence• timesame at the occured severities thebetween Dependence•cellsrisk many affecting events common via theDependence•
, and sfrequencie thebetween Dependence•)](|[)(:(ES) shorfall Expected•
failmay ationdiversificformally and measure coherent a not is },)(,min{)()( :VaR•
)C()C()C( :capitala in ationdiversific Possible•
...:
11
1
)(2
1
)2(1
1
)1(
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jiZZ
jiNNZVaRZZEZES
zFzFZVaR
ZZZ
XXXZZlossannualtotal
ji
ji
ZZ
K
KN
i
Ki
N
ii
N
ii
K
kk
≠
≠>=
≥==
+…+≤
+++==
−
====∑∑∑∑
αα
α αα
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Example: dependence between frequency profiles;dependence between severity profiles
.,between copula)( ;,between copula)(
.parameter copulaGaussian vs),(n correlatiorank sSpearman'(2)(1)(2)(1)
)2()1(S
μμλλ
ρρ
−∗−o
ZZ
copula via,,between dependence
)1,1(~ and )1.0,2(~),10,4(~
),(~)(),(~
)( and )(
)()()(
)()()(
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)()()(
1
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jt
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jt
jt
jt
jt
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is
jt
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jtN
s
js
jt
itN
s
is
it
GammaNGamma
LNtXPoissonN
tXZtXZ
σμλ
σμλ
σμλ
•
•
•
∑=∑===
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Parameter Risk (uncertainty of parameters)
densityposterior the),()|()|(]ˆˆ[
MLEestimator,point a is ˆ);ˆ|(ofquantile999.0ˆ)|(ofquantile999.0ˆ
ondistributipredictive full)|()|()|(,...,1 nsobservatiopast ),(
; year in loss)(
999.0999.0
1999.0
1999.0
11
1
θθYYθ
θθ
Y
θYθθYNXY
ππ
ϕ
πϕ
hQQEbias
ZgQ
ZQ
dZgZMt
ttXZ
BM
MB
MM
tN
iit
∝•−=
−•
−•
−∫ ×=•=−=•
−∑=
+
+
++
=
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Parameter Risk (uncertainty of parameters)
0%
50%
100%
150%
200%
250%
5 10 15 20 25 30 35 40Year
% b
ias
LognormalPareto
Relative bias in the 0.999 quantile estimator induced by the parameter uncertainty vs number of observation years. (Lognormal) - losses were simulated from Poisson(10) and LN(1,2). (Pareto) – losses were simulated from Poisson(10) and Pareto(2) with L=1.
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Modelling commodities/interest rates: state-space models
• Measurement Equation:• Transition Equation:
ttTtttTTt
ttttt
ttt
ttt
Ttttt
tTCtTBtTAThFSEF
dtdWdWEdWdtd
dWdtd
thSFS
χξξχ
ρσδκλχ
σωξλμξ
χξ
χξ
χ
ξ
)()()()(ln],|[
][;][
][
)(lnprices futures rates, long/short,price;spot
,,
)2()1()2(21
)1(1
,
−+−+−+=⇒=
=+−−=
+−−=
++=
−−−
• Commodity spot models: e.g. 2-factor long-short
eXBAF ttrrrr
+×+= ˆ
εrrrr
+×+=+ tt XTMX ˆ1
• Non-Gaussian models/fitting option prices – calibration requires non-linear Kalman filter, particle filter/SMC
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Seasonal and non-seasonal commodities
Crude Oil Future Prices vs maturity month
$60
$62
$64
$66
$68
$70
1 3 5 7 9 11
fitted on 24/02/2006obs on 24/02/2006
Crude Oil standard deviation vs maturity month
20%
22%
24%
26%
28%
30%
32%
1 3 5 7 9 11
fittedobserved
Soy Beans Future Prices vs maturity
$500
$520
$540
$560
$580
$600
1 2 3 4 5 6 7
fitted on 19/10/2004observed on 19/10/2004
standard deviation vs maturity
18%19%20%21%22%23%24%25%26%27%
1 2 3 4 5 6 7
observedfitted
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Pricing Exotic Options: Stochastic Volatility, Implied Volatility Smile
0
200
400
600
800
1000
1200
1400
1600
1800
24/07/1998 6/12/1999 19/04/2001 1/09/20020
0.1
0.2
0.3
0.4
0.5
0.6S&P500Historic vol
800
830
860
890
920
950
980 0.14
0.26
0.39
0.51
0.15
0.2
0.25
0.3
0.35
0.4
implied volatility
strike
maturity
Local Volatility models (e.g. Dupire 1993)Stochastic Volatility and Jump-diffusion models (e.g. Merton 1976,
Heston 1993)
S&P500
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Heston stochastic volatility model (1993)
0,)(
;0Im,)(
]0,max[)( payoff optionPut
1,)(
;1Im,)(
],0,max[)( payoff option Call
)( ;)( ;)()(
:approx or PDF Fourier inverse via price Option
)]()()(exp[),,|,,(
ln ),,,|,,(density tionfor transi FunctionsticCharacteri)(
)(
process neutral-Risk
1
21
1
1
21
1
30201000
000
>+
−=<−
−=
−=•
−<+
−=>−
−=
−=•
====
•
++==
=•
+−=
+−=
•
∫
∫
∫∫∫∫
∫
−∞
+∞−
+−+
−∞
+∞−
+−+
−
adkikk
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Kh
SKxh
adkikk
KpCkikk
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KSxh
dxxpepdxxhehdkhpdxxhxpQ
CvCxCdxdvtvxtvxpep
SXtvxtvxpdZVdtVdV
dWVSdtqrSdS
ia
ia
ik
k
ik
k
ia
ia
ik
k
ik
k
ikxk
ikxkkk
ikxk
tttt
ttttt
π
π
τττ
ξθω
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Heston model - Calibration via today’s prices
impl vol vs strike
12.5%
13.5%
14.5%
0.516 0.526 0.536 0.546
observed at 7daysfitted at 7days
impl vol vs strike
12.5%
13.5%
14.5%
0.416 0.516 0.616
observed at 367daysfitted at 367days
impl vol vs strike
12.5%
13.5%
14.5%
0.516 0.526 0.536 0.546
observed at 7days
fitted at 7daysimpl vol vs strike
12.5%
13.5%
14.5%
0.416 0.466 0.516 0.566 0.616 0.666
observed at 367daysfitted at 367days
Constant model parameters, US$/AU$
Time-dependent model parameters, US$/AU$
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Local volatility model, Dupire 1993
volimplied is .
1
22),(
//))()(()(/2),( :function Volatility
0)))()(()),((),,,( :eq Kolmogorov Fwd.
),,,(),,,( :density neutral-Risk
]0,)([)),(())(( :payoff Call
,),,,()(),( :priceoption Vanilla
).(),()]()([)(/)( :process neutral-Risk
2
12
22
2
1
2
2222
2
222
21
2
2
0
θθθθθ
θθθθθσ
σ
σ
σ
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛∂∂−
∂∂+⎥⎦
⎤⎢⎣⎡
∂∂+
∂∂
++∂∂
=
∂∂∂∂−++∂∂
=
=∂−∂
+∂
∂−
∂∂
∂∂
=
−==
=
+−=
∫∞
TK
dK
TKK
TKd
KTrK
TT
TK
KCKKCTqTrKCTqTCTK
uupTqTr
upuTu
TTutSp
KTKtSCTKtSp
KTSMaxTTSCTSh
duTutSpuhtSQ
tdWtSdttqtrtStdS
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Local volatility model – Exotic Option Pricing
element finite ,difference finite :methods PDENumerical
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).(),()]()([/]0,max[payoff call e.g.)];(Payoff[),( :price Option
2
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σ
CSIRO Mathematical & Information Sciences www.cmis.csiro.auJoint work with M.Wüthrich (ETH Zurich) and G.Peters (UNSW/CSIRO)
Claims Reserving (non-life insurance), solvency requirements, claims development triangle
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
- predictor for and estimator for
Mean Square Error
of Prediction
“best estimate” of reserveBayesian context – variance decomposition
is model parameter vector modelled as random variable
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Claims reserving: Tweedie’s compound Poisson model
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Claims reserving – expected reserves (ER), process variance (PV), estimation error (ER). Bayesian (MCMC) vs Maximum Likelihood
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Research topics for collaboration
• Combining different data sources: internal & external data with expert opinions (credibility theory, Bayesian techniques)
• Dependence between risks: copula methods, structural models• Expert elicitation (Bayesian networks) • Extreme Value Models (Modelling distribution tail)• Efficient Markov Chain Monte Carlo, ABC MCMC, Monte Carlo, finite
element/finite difference methods • State-space models (Kalman/particle filters/SMC)
• Pattern recognition – trading strategies • Stochastic/local volatility models• Modelling operational/market/credit risks/insurance risks• Pricing exotic options• Modelling commodities, interest rates, • Portfolio asset allocation
CSIRO Mathematical & Information Sciences www.cmis.csiro.au
Recent journal publications
• G. W. Peters, P.V. Shevchenko and M.V. Wüthrich (2009). Chain Ladder Method: Bayesian Bootstrap versus Classical Bootstrap. Submitted to Insurance: Mathematics and Economics.
• G. W. Peters, P. V. Shevchenko and M. V. Wüthrich (2009). Model uncertainty in claims reserving within Tweedie's compound Poisson models. ASTIN Bulletin 39.
• P. V. Shevchenko (2008). Implementing Basel II Loss Distribution Approach for operational Risk. Submitted to Applied Stochastic Models in Business and Industry.
• Peters, G., P. Shevchenko and M.Wuthrich (2009). Dynamic operational risk: modelling dependence and combining different data sources of information. J. of Op Risk
• Shevchenko, P. (2008). Estimation of Operational Risk Capital Charge under Parameter Uncertainty. The Journal of Operational Risk 3(1), 51-63.
• Luo, X., P. V. Shevchenko and J. Donnelly (2007). Addressing Impact of Truncation and Parameter Uncertainty on Operational Risk Estimates. The J. of Op. Risk 2(4), 3-26.
• D. D. Lambrigger, P.V. Shevchenko and M. V. Wüthrich (2007). The Quantification of Operational Risk using Internal Data, Relevant External Data and Expert Opinions. J. of Op. Risk 2(3), 3-27.
• Bühlmann,H., P. Shevchenko and M. Wüthrich. A “Toy” Model for Operational Risk Quantification using Credibility Theory. The J. of Operational Risk 2(1), 3-19, 2007.
• Shevchenko, P. and M. Wüthrich (2006). Structural Modelling of Operational Risk using Bayesian Inference: combining loss data with expert opinions. J. of Op. Risk 1(3), 3-26.
www.cmis.csiro.au/Pavel.Shevchenko
Thank you
CSIRO Mathematical & Information SciencesPavel Shevchenko
Email: [email protected]/Pavel.Shevchenkowww.csiro.au/people/Pavel.Shevchenko.html